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The Joy of x: A Guided Tour of Math, from One to Infinity Hardcover – October 2, 2012
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Guest Review by Janna Levin
Janna Levin is a Professor of Astronomy and Physics at Barnard College of Columbia University. She has contributed to an understanding of black holes, the cosmology of extra dimensions, and gravitational waves in the shape of space time. She is the author of the popular-science book, How the Universe Got Its Spots and a novel, A Madman Dreams of Turing Machines, which won the PEN/Bingham prize. Janna was recently named a Guggenheim Fellow (2012).
I loved this beautiful book from the first page.
Mathematicians are in a peculiar predicament. Mathematical beauty is patent to them. And in the perception of that beauty is pleasure, is joy. But that pleasure is not easily shared. Mathematical beauty eludes many others, or even most others.
Steven Strogatz wants to share that joy. He sees the beauty of pi and 0 and infinity. But he doesn’t want to impose his impressions on you or to report on the view from his privileged perspective. He wants you to see it too. He doesn’t want to argue that mathematics is creative and beautiful. He wants you to experience the visceral pleasure for yourself.
To that end, he disassembles mathematics as a discipline, both feared and revered, and reassembles mathematics as a world, both accessible and magical.
If you have never braved this grand world, put away your math anxiety, your preconceptions. This book is the most welcoming entree to mathematical thinking that I know of.
If you have braved this grand world, you will find a collection of gems, new ways of inhabiting the domain. Strogatz links historical anecdotes to new insights, as though the math itself is sculptural, composed of forms that are simultaneously familiar and ethereal. The logic seems effortless so that each module snaps into its complement with a gratifying click.
This book is a rebuttal to the accusation that mathematical abstraction is cold or inhuman. Mathematics is no more intrinsically cold or inhuman than language. And Strogatz lends a warmth and humanity to both.
The Joy of x is, well, a joy.
When Strogatz invites grade-schoolers to construct Möbius strips with scissors, crayons, and tape, he is not expecting them to discover revolutionary new mathematical principles. But he does expect them to experience the kind of intellectual joy that sustains a lifetime of mathematical inquiry. Readers share that joy by joining Strogatz on a high-spirited romp through complex numbers, standard deviations, infinite sums, differential equations, and other mathematical playgrounds. The math arrives in such delightful episodes—a hike through a snow-covered field, for example, or an excited dinner conversation over symbols scribbled on a napkin—and is so often connected to poetry, sports, and popular TV shows that even math phobes will find themselves swept up in the fun. (Who knew that The Sopranos could help us fathom calculus?) To be sure, Strogatz occasionally points well-schooled readers to the rigorous analyses identified in his endnotes. But even those reluctant to venture into deeper waters will finish this book with a new relish for mathematics as a thrilling adventure, not a dreary chore. --Bryce Christensen
Top customer reviews
In The Joy of x, Strogatz has done a masterful job as our tour guide through the elements of mathematics, and he's done it without "dumbing it down" or making it just another refresher course for the subject. He presented the various mathematical elements and concepts in fresh new ways, but he clearly expected the reader to exercise their mind to understand. The reward was a new appreciation of the beauty of mathematics and for how our knowledge of the subject advanced in fits and starts over several thousand years.
The book has six parts, each presenting certain elements of mathematics: Numbers, Relationships, Shapes, Change, Data, and Frontiers. These sections represent a grand tour through the history and development of mathematics, including the practical - and some whimsical - applications. Never again will I fall into the trap of bungling the answer to the classic "If three men paint three fences in three hours, how long will it take for one man to paint one fence?" (answer: 3 hours). Now I understand why a piece of paper can't be folded in half more than 7-8 times, and how a high school junior was able to beat the record using a monstrously long roll of... toilet paper! I know how Luke could guarantee himself a win over Darth Vader in a game of laser tag (hint: it involves a conic section). For young lovers, mathematics could help in finding the perfect mate (if you make a few simplistic assumptions, that is). And if the prosecution in the O.J. Simpson murder trial had understood probability and statistics, could they have gotten a conviction?
As enjoyable as the first five sections of the book were, my favorite section was the last, "Frontiers," where the author covered topics including prime numbers, where I learned that no one has ever found an exact formula to find primes; group theory, which bridges the arts and sciences; topology; spherical geometry; and infinite series. This section presented some fascinating ideas. For example, group theory suggests how to get the most even wear from a mattress and confirms the old mnemonic "spin in the spring, flip in the fall." For topology, the famous Möbius strip is examined. I thought I understood the properties of a Möbius strip, but they're actually more remarkable than I would have guessed. And the most mind-blowing concept was that some infinities are larger than others. This finding, which was bitterly contested at the time, is brilliantly demonstrated with a parable named the Hilbert Hotel.
I don't always read all of the footnotes or endnotes in a book, but the endnotes in The Joy of x are not to be missed. There are dozens of links to websites and online videos that demonstrate or expound on the concepts presented in the book. Some of these were so intriguing that I spent a couple of hours being spellbound by them.
For anyone who's been disappointed by other math books written for laypersons, The Joy of x may be the book they've been hoping for. With keen insight, a light touch, and a bit of humor, author Steven Strogatz has written a splendid book for anyone who wants a broader understanding of mathematics.
Note: I read an advance reader copy of this book provided by the publisher through NetGalley.
Steven Strogatz shows us the basic concepts of numbers and math, building from the simple: Sesame Street characters counting fish, to the mind boggling: some infinities are larger than others.
We first learn about the power of numbers when we go from calling out "fish, fish, fish" for each fish we see to grouping them together in the abstract idea of "three fish". Numbers are abstract ideas we use to stand in so we can easily measure and compare things. Once we build a set of relationship rules (addition, subtraction) we continue to develop methods of relationships. For example we build fractions as "ratios of integers - hence teir technical name, rational numbers." (p 29). These rules continue to build upon one another and take us through algebra and geometry to calculus. As an example Strogatz demonstrates that adding "all the consecutive odd numbers, starting from 1: The sums above, remarkably, always turn out to be perfect squares" (p10).
My biggest takeaway from the book is that when you have a hammer, everything looks like a nail. You can only use the tools in your belt to solve the problems you encounter. And worse if you do use the tools in your belt you may get the wrong answer. Or worse yet; you may have the correct tool set but use them dishonestly to misdirect people - those people like me - who didn't study enough math.
An example of that is statistics, where figures lie and liers figure. Most of us have at least a passing understanding of normal distributions (bell curves). They "can be proven to arise whenever a large number of mildly random effects of similar size, all acting independently, are added together. And many things are like that." (p 178). Many, but not all. "[P]lenty of phenomena deviate from this pattern yet still manage to follow a pattern of their own." (p 178). But we are more comfortable with the normal distributions and have the tools (the mean average) to work with them. In Power-law distributions the "modes, medians, and means do not agree because of the skewed, asymmetrical shapes of their L-curves. President Bush made use of this property when he stated that his 2003 tax cuts had saved families an average of $1,586 each. Though that is technically correct, he was conveniently referring to the mean rebate, a figure that averaged in the whopping rebates of hundreds of thousands of dollars received by the richest 0.1 percent of the population. The tail on the far right of the income distribution is known to follow a pwoer law, and in situations like this, the mean is a misleading statistic to use because it's far from typical. Most families, in fat got less that %650. The median was a lot less than the mean." (p. 180)
I've been intimidated by calculus but Strogatz does an effective job of making it approachable - you won't learn calculus from the book but you'll get a glimmer of understanding. If we want to find the area of a circle we start by fitting a square inside and calculate its area; then turn it into an 8 sided figure - like slices of a pizza - and calculating its area we get closer yet. And so on as the number of pie slices approaches infinity.
Strogatz wraps things up with the theory of infinite sets using the illustration of the Hilbert Hotel which is always full but there is always room for one more. I can't do it justice here but he shows how the infinity of the real numbers between 0 and 1 is bigger than the infinity of whole numbers. Whaaaat?
Finally I became acquainted with the "recreational mathemusician" Vi Hart through this book. She is a video illustrator who does some marvelous work demonstrating mathematic concepts. Even if you don't read this book (which you totally should), check out Vi Harts story of Wind and Mr. Ug; a couple of two dimensional beings who live on a transparent Möbius strip.