What do you think?
Rate this book
316 pages, Hardcover
First published October 2, 2012
In these 30 short essays--a couple of which I had read before in his Time column--Strogatz begins at the beginning (with the concept of counting) and winds his way through everything from basic algebra to calculus to advanced topics like group theory and topology, discussing each topic in a way that is not only friendly and approachable for the mathematical neophite (or phobic), but fascinating. And for all that the book is aimed at a general audience, I have to admit that I learned a few fascinating things about some topics that I didn't even learn in my advanced semester-long college classes. (Did you know there are real-world applications from infinite series? I didn't!)
So yes, this is a book about math, but it isn't just for math lovers. In fact, it's probably more for people who felt like they "never really got it" in school but are maybe just a little intrigued and kind of want another crack at it (in a way that doesn't involve doing homework). I also think it makes a GREAT resource for math teachers. (I used the two calculus essays as introductions to each semester of the course, differential & integral respectively. They give a really great, 30,000 ft overview that I thought might help the students see what it was we were really doing and why before we got bogged down in problem sets.)
The great innovation here is that even though this system is based on the number 10, there is no single symbol reserved for 10. Ten is marked by a position—the tens place—instead of a symbol. The same is true for 100, or 1,000, or any other power of 10. Their distinguished status is signified not by a symbol but by a parking spot, a reserved piece of real estate. Location, location, location.You can almost hear the author chuckle as your read these bons mots; maybe you will hear them in the voice of your dad as he assures you that, “You’d be disappointed if I didn’t say it,” while you roll your eyes from teenaged embarrassment. I sure did.
As the numbers inside the logarithms grew multiplicatively, increasing tenfold each time from 100 to 1,000 to 10,000, their logarithms grew additively, increasing from 2 to 3 to 4. Our brains perform a similar trick when we listen to music. The frequencies of the notes in a scale—do,re, mi, fa, sol, la, ti, do—sound to us like they’re rising in equal steps. But objectively their vibrational frequencies are rising by equal multiples. We perceive pitch logarithmically.But The Joy of X is not simply information transfer sweetened with sincerity. There is a dark side to math, the spooky forest of numbers and incomprehensibility that frightened so many of us into a B.A. in English Lit. For those willing to return to the road not taken, there are forty pages of endnotes:
The analysts of the 1800s identified the underlying mathematical cause of the Gibbs phenomenon. For functions (or, nowadays, images) displaying sharp edges or other mild types of jump discontinuities, the partial sums of the sine waves were proven to converge pointwise but not uniformly to the original function. Pointwise convergence means that at any particular point x, the partial sums get arbitrarily close to the original function as more terms are added. So in that sense, the series does converge, as one would hope. The catch is that some points are much more finicky than others. The Gibbs phenomenon occurs near the worst of those points—the edges in the original function.These notes are here to remind a reader, flush with feelings that math is for the people—doable by everyone in an egalitarian utopia of numbers and equations and formulae—that maybe math is not quite that simple. The Joy of X just makes it seem so clear and enjoyable, like an organized hike up gentle mountain trail. The path has been worn clear of debris by the generations of travelers before you, and your tour guide is so witty and knowledgeable that before you know it you're standing next to a sign marked "Scenic Overlook," posing in front of the same backdrop as countless other tourists before you. You feel like you've done something: "I've hiked a mountain!" But no. You've trod a path that's existed for millennia, and while it may be a good first tour, experienced outdoorsy-types would cluck their tongues and shake their heads if you started calling yourself a hiker. As time passes, only the photo remains; a vague memory of the brief moment your comprehension of mathematics sufficed for a picturesque vista. By contrast, the endnotes lead you to a sheer cliff, toss you a rope, a compass, and a pocket knife, and ditch you in the middle of the Appalachians. Just like this extended metaphor, math is a struggle. Unlike this metaphor, math can often be elegant.
In the early part of the ninth century, Muhammad ibn Mus al-Khwarizmi, a mathematician working in Baghdad, wrote a seminal textbook in which he highlighted the usefulness of restoring a quantity being subtracted by adding it to the other side of the equation. He called this process al-jabr (Arabic for “restoring”), which later morphed into “algebra.” Then, long after his death, he hit the etymological jackpot again. His own name, al-khwarizmi, lives on today in the word “algorithm.”Well, good, then. One would think this would be common knowledge. Really, both algebra and algorithm from the same person? That's impressive. "Restoring" even makes sense—it's what you do while balancing equations in algebra. Many students, past and present, might benefit from having context to frame the math ex nihilo that is constantly being smashed into their faces.