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How Not to Be Wrong: The Power of Mathematical Thinking, by Jordan Ellenberg
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The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands
The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it.
Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?
How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.
Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
- Sales Rank: #2142 in Books
- Brand: Ellenberg, Jordan
- Published on: 2015-05-26
- Released on: 2015-05-26
- Original language: English
- Number of items: 1
- Dimensions: 8.40" h x .99" w x 5.50" l, .0 pounds
- Binding: Paperback
- 480 pages
From Booklist
*Starred Review* How many home runs can fans expect a league leader to hit after the All Star break? Why is the most handsome man around often the rudest? By exploring questions such as these, Ellenberg breaks through the widespread perception of mathematics as a narrowly academic pursuit, hopelessly irrelevant to the lives of ordinary people. Readers will indeed marvel at how often mathematics sheds unexpected light on economics (assessing the performance of investment advisors), public health (predicting the likely prevalence of obesity in 30 years), and politics (explaining why wealthy individuals vote Republican but affluent states go for Democrats). Relying on remarkably few technical formulas, Ellenberg writes with humor and verve as he repeatedly demonstrates that mathematics simply extends common sense. He manages to translate even the work of theoretical pioneers such as Cantor and G�del into the language of intelligent amateurs. The surprises that await readers include not only a discovery of the astonishing versatility of mathematical thinking but also a realization of its very real limits. Mathematics, as it turns out, simply cannot resolve the real-world ambiguities surrounding the Bush-Gore cliff-hanger of 2000, nor can it resolve the much larger question of God’s existence. A bracing encounter with mathematics that matters. --Bryce Christensen
Review
Manil Suri,�The Washington Post:
“Brilliantly engaging.... Ellenberg’s talent for finding real-life situations that enshrine mathematical principles would be the envy of any math teacher. He presents these in fluid succession, like courses in a fine restaurant, taking care to make each insight shine through, unencumbered by jargon or notation. Part of the sheer intellectual joy of the book is watching the author leap nimbly from topic to topic, comparing slime molds to the Bush-Gore Florida vote, criminology to Beethoven’s Ninth Symphony. The final effect is of one enormous mosaic unified by mathematics.”
Mario Livio, The Wall Street Journal:
“Easy-to-follow, humorously presented.... This book will help you to avoid the pitfalls that result from not having the right tools. It will help you realize that mathematical reasoning permeates our lives—that it can be, as Mr. Ellenberg writes, a kind of 'X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world.'”
Evelyn Lamb, Scientific American:
“Witty, compelling, and just plain fun to read.... How Not to Be Wrong can help you explore your mathematical superpowers.”
Laura Miller, Salon:
“A poet-mathematician offers an empowering and entertaining primer for the age of Big Data.... A rewarding popular math book for just about anyone.”
Nature:
“Mathematicians from Charles Lutwidge Dodgson to Steven Strogatz have celebrated the power of mathematics in life and the imagination. In this hugely enjoyable exploration of everyday maths as 'an atomic-powered prosthesis that you attach to your common sense', Jordan Ellenberg joins their ranks. Ellenberg, an academic and Slate’s ‘Do the Math’ columnist, explains key principles with erudite gusto—whether poking holes in predictions of a US 'obesity apocalypse', or unpicking an attempt by psychologist B. F. Skinner to prove statistically that Shakespeare was a dud at alliteration.”
Times Higher Education:
“A fresh application of complex mathematical thinking to commonplace events.... How Not to Be Wrong is beautifully written, holding the reader’s attention throughout with well-chosen material, illuminating exposition, wit and helpful examples. I am reminded of the great writer of recreational mathematics, Martin Gardner: Ellenberg shares Gardner’s remarkable ability to write clearly and entertainingly, bringing in deep mathematical ideas without the reader registering their difficulty.”
Kirkus Reviews:
“The author avoids heavy jargon and relies on real-world anecdotes and basic equations and illustrations to communicate how even simple math is a powerful tool….[Ellenberg]writes that, at its core, math is a special thing and produces a feeling of understanding unattainable elsewhere: ‘You feel you’ve reached into the universe’s guts and put your hand on the wire.’ Math is profound, and profoundly awesome, so we should use it well—or risk being wrong….Witty and expansive, Ellenberg’s math will leave readers informed, intrigued and armed with plenty of impressive conversation starters.”
Booklist:
“Readers will indeed marvel at how often mathematics sheds unexpected light on economics (assessing the performance of investment advisors), public health (predicting the likely prevalence of obesity in 30 years), and politics (explaining why wealthy individuals vote Republican but affluent states go for Democrats). Relying on remarkably few technical formulas, Ellenberg writes with humor and verve as he repeatedly demonstrates that mathematics simply extends common sense. He manages to translate even the work of theoretical pioneers such as Cantor and G�del into the language of intelligent amateurs. The surprises that await readers include not only a discovery of the astonishing versatility of mathematical thinking but also a realization of its very real limits. Mathematics, as it turns out, simply cannot resolve the real-world ambiguities surrounding the Bush-Gore cliff-hanger of 2000, nor can it resolve the much larger question of God’s existence. A bracing encounter with mathematics that matters.”
Steven Pinker, Johnstone Family Professor of Psychology, Harvard University; author of How the Mind Works:
“The title of this wonderful book explains what it adds to the honorable genre of popular writing on mathematics. Like Lewis Carroll, George Gamow, and Martin Gardner before him, Jordan Ellenberg shows how mathematics can delight and stimulate the mind. But he also shows that mathematical thinking should be in the toolkit of every thoughtful person—of everyone who wants to avoid fallacies, superstitions, and other ways of being wrong.”
Steven Strogatz, Schurman Professor of Applied Mathematics, Cornell University, and author, The Joy of x:
“With math as with anything else, there’s smart, and then there’s street smart. This book will help you be both. Fans of Freakonomics and The Signal and the Noise will love Ellenberg’s surprising stories, snappy writing, and brilliant lessons in numerical savvy. How Not to Be Wrong is sharp, funny, and right.”
John Allen Paulos, author of Innumeracy and A Mathematician Reads the Newspaper:
“Through a powerful mathematical lens Jordan Ellenberg engagingly examines real-world issues ranging from the fetishizing of straight lines in the reporting of obesity to the game theory of missing flights, from the relevance to digestion of regression to the mean to the counter-intuitive Berkson’s paradox, which may explain why handsome men don’t seem to be as nice as not so handsome ones. The coverage is broad, but not shallow and the exposition is non-technical and sprightly.”
Timothy Gowers:
“Jordan Ellenberg is a top mathematician and a wonderful expositor, and the theme of his book is important and timely. How Not to Be Wrong is destined to be a classic.”
Rebecca Newberger Goldstein, author of Plato at the Googleplex:
“Jordan Ellenberg promises to share ways of thinking that are both simple to grasp and profound in their implications, and he delivers in spades. These beautifully readable pages delight and enlighten in equal parts. Those who already love math will eat it up, and those who don’t yet know how lovable math is are in for a most pleasurable surprise."
Danica McKellar, actress and bestselling author of Math Doesn’t Suck and Kiss My Math:
"Brilliant and fascinating! Ellenberg shows his readers how to magnify common sense using the tools usually only accessible to those who have studied higher mathematics. I highly recommend it to anyone interested in expanding their worldly savviness—and math IQ!"
The Guardian
“How Not to Be Wrong is a cheery�manifesto for the utility of mathematical thinking. Ellenberg's prose is a delight – informal and robust, irreverent yet serious. Maths is "an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength," he writes. Doing maths "is to be, at once, touched by fire and bound by reason. Logic forms a narrow channel through which intuition flows with vastly augmented force.”
About the Author
Jordan Ellenberg is the John D. MacArthur Professor of Mathematics at the University of Wisconsin-Madison and a 2015 Guggenheim fellow. He has lectured around the world on his research in number theory and delivered one of the invited addresses at the 2015 Joint Mathematics Meetings, the largest math conference in the world. His writing has appeared in�The New York Times,�The Washington Post,�The Wall Street Journal,�The Boston Globe,�Wired,�and�The Believer, and he has been featured on the Today show and NPR’s�All Things Considered. He writes a popular column called “Do the Math” for�Slate.
Most helpful customer reviews
228 of 243 people found the following review helpful.
"Mathematics is the extension of common sense by other means."
By BHB
I run across a lot of books that I add to my to-be-read list and then forget about until after their publication dates or I stumble upon the book in the library or bookstore. How Not to Be Wrong was initially one of those books, but it sounded so good that I found myself obsessively thinking about it and started a search for a pre-publication copy. Since I'm not a librarian, didn't win a copy via First Reads, and don't have friends at Penguin Press, it took some time and effort, but having procured a copy and read it, I can say that it was well worth my time and $6.00. How Not to Be Wrong is a catchy title, but for me, this book is really about the subtitle, The Power of Mathematical Thinking.
Ellenberg deftly explains why mathematics is important, gives the reader myriad examples applicable to our own lives, and also tells us what math can't do. He writes, “Mathematics is the extension of common sense by other means”, and proceeds to expound upon an incredible number of interesting subjects and how mathematics can help us better understand these topics, such as obesity, economics, reproducibility, the lottery, error-correcting codes, and the existence (or not) of God. He writes in a compelling, explanatory way that I think anyone with an interest in mathematics and/or simply understanding things more completely will be able to grasp. Ellenberg writes “Do the Math” for Slate, and it's evident in his column and this book that he knows how to explain mathematical ideas to non-mathematicians, and even more so, seems to enjoy doing so with great enthusiasm. I won't pretend that I understood everything discussed in this book, but it's such an excellent book that I also bought the hardcover (so I have an index which my pre-pub copy does not), and reread the book so I do have a much more thorough understanding. I've wished for a book like this for a long time, and I'd like to thank Jordan Ellenberg for writing it for me!
312 of 359 people found the following review helpful.
If there was one thing I was reminded of in reading this book its that I shouldn't have trusted the five star reviews....
By Nom de Plume
Review edited: 3/15/2015
Let me save you your money and give you the two best pieces of advice in this book: instead of looking for reasons why you could be right, look for reasons why you could be wrong. Humans are prone to confirmation bias--trying to confirm what we want to be true. Determine where your biases are and attempt to remove them. If you don't want to be wrong, constantly look for reasons why you could be wrong. Second, always evaluate the assumptions that you are making and determine whether or not those assumptions are true. The best part of the book was at the very beginning with the chapter on Abraham Wald, which explains this lesson beautifully. If you want to read that story, check this book out from the library and save yourself the money...the rest of the book was largely a waste of my time and money.
Unfortunately, I made both those mistakes when purchasing this book. I assumed that this would be a highly logical book with mathematical reasoning....wrong. It amazes me that an author, writing about how to not be wrong showed so many examples of biased and illogical thinking. Other reviewers have gone into the political bias but there were other claims that I found to be a bit more troubling. Everything you do either prevents or causes cancer? You've got to be kidding me.....so, which end of this false dichotomy does reading "how to not be wrong" get me? ......"The null hypothesis is almost always false".....nope, wrong again. Unfounded, illogical, and biased claims abound in this book.
The irony here is that you likely can't take my review seriously because my review is likely just as biased as all the others. In order for you to determine whether or not "how to not be wrong" is in fact a book worth your time and money is for you to buy it and evaluate it for yourself. Simply taking my word for it would be wrong. So, given this fact, I highly recommend you rent this from your local library rather than believing the 5 star reviews (wanting it to be as good as they say it is and as good as I hoped it would be) or reviews like mine that simply were unimpressed. And that, my friends, is how to not waste your money!
*Let me be clear in that I do think that this book does have value. I think it does teach the importance of mathematical reasoning and each chapter does have value in that regard. The question you have to ask is whether you can get past the authors biased claims (he really does have a political bias, though who doesn't?) and whether you can recognize instances when he is making assumptions that aren't verifiable (cancer, stocks, etc.). This book can be a very good exercise in mathematical reasoning if you bring the knowledge that not everything the author states is going to be absolutely correct and question his claims. Certainly no one is going to be perfect when it comes to logical/mathematical reasoning, even mathematicians can exhibit flaws in logical reasoning. However, the purpose of my review is that if you are looking for books to teach you this and teach you well, there are better sources. Such as the one I mentioned previously.
If you are truly interested in improving your logic and using mathematical thinking to "not be wrong" then a much much better way to invest your money is in "Your deceptive mind" by Professor Steven Novella. Yes, its more expensive but absolutely fantastic.
142 of 165 people found the following review helpful.
You Simply Won't Believe How Much This Book Will Change Your Life
By Jeffrey W Hatley
I've already been recommending this book to family and friends, so I thought I'd take a few moments to recommend it to strangers on the internet, too.
This book, as anyone who is familiar with Jordan Ellenberg's writing (or speaking!) would expect, is written in an entertaining, witty, and engaging style. Each chapter of the book is framed by one or two major, motivating questions, such as:
- What parts of military aircraft should get the most armor?
- Is it ever a good idea to play the lottery?
- How should votes be counted in a democracy?
The answers that mathematical thinking asks you to accept are often surprising and unintuitive, but Jordan guides the reader through the fog of potentially-complicated arguments with a conversational style rife with clear, succinct examples and amusing historical anecdotes. In the hands of other writers, the mathematics in this book may be dull, or technical and complicated, or all of these things; but with How Not To Be Wrong, Jordan has instead created a book that you will eagerly and (mostly) effortlessly consume.
To put it another way: Steven Pinker said that "assumption of equality between writer and reader makes the reader feel like a genius, [while] bad writing makes the reader feel like a dunce." Jordan Ellenberg makes the reader feel like a genius.
Finally, regarding another reviewer's comments about the author's "liberal bias", I'd like to point out that I had the exact opposite impression while reading this book. Whenever politics were considered, I thought Jordan was even-handed and stuck to the mathematics at hand without wading into any political commentary. While I have liberal political ideals, and I avoid talking about politics with the more conservative members of my family, I would not feel uncomfortable recommending or gifting this book to any of them. This simply is not a book about politics, and I'm surprised that anyone would would have their political feathers ruffled when reading it.
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