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How Not to Be Wrong: The Power of Mathematical Thinking [Kindle Edition]

Jordan Ellenberg
4.1 out of 5 stars  See all reviews (115 customer reviews)

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Book Description

The Freakonomics of matha 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.






Editorial Reviews

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 Gödel 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

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 Gödel 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!"

Product Details

  • File Size: 8710 KB
  • Print Length: 466 pages
  • Page Numbers Source ISBN: 184614678X
  • Publisher: The Penguin Press (May 29, 2014)
  • Sold by: Penguin Group (USA) LLC
  • Language: English
  • ASIN: B00G3L6JQ4
  • Text-to-Speech: Enabled
  • X-Ray:
  • Lending: Not Enabled
  • Amazon Best Sellers Rank: #8,476 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
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Customer Reviews

4.1 out of 5 stars
(115)
4.1 out of 5 stars
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Most Helpful Customer Reviews
151 of 160 people found the following review helpful
By BHB
Format:Hardcover|Verified Purchase
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!
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83 of 96 people found the following review helpful
Format:Hardcover|Verified Purchase
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.
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15 of 17 people found the following review helpful
5.0 out of 5 stars An Acquired Taste, So Don't Give Up Too Soon! June 27, 2014
Format:Hardcover|Verified Purchase
You'll start reading this book thinking there will be a lot of juicy math on odds vs. utility functions in decision theory, then toss it out in disgust when you find you're reading a snail-paced "lives of the Saints in Probability..."

BUT IF you toss it, you'd be WRONG just like the book's title! Ok, I'm with George Box that all models are wrong but some are useful, so in all humility, even if our thinking is n-dimensional and nonlinear, our headlights still don't go out centuries, and the law of unintended consequences will inevitably rear it's fearsome head. So yes, I know I'm gunna be wrong more than right even reading this gem of a book.

It gets FUN! As you read on, Jord gets into deeper and deeper math, and most significantly, starts to COMBINE stats, geometry, differential equations, etc. in eclectic, multi-disciplinary fields, which are much more like real life than academic exercises. It is not only math that has a new twist every hour these days, it is the combinations of fields (as in vocations and disciplines, not quantum fields) that is making math more and more relevant.

I'm not one to discount the gut, heart, tradition or even intuition, but it really is enlightening to take a little more quant view at our normal evaluations of everyday spin. Yes, the author does have a bit of a left bent, but heck, those are just examples, and you'd have to be pretty emotion driven not to see how easily his logic applies to ANY "position." I see a LOT of tongue in cheek in this book and a LOT of both wonder and just plain great story telling-- please don't pass on this book if you're bright but not necessarily a policy wonk!
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Most Recent Customer Reviews
3.0 out of 5 stars Would have been better without politics!
The principles and ideas the author puts forth are engaging and thought provoking. He does a good job explaining most of what he covers, although once in a while I felt the urge to... Read more
Published 3 days ago by Ingeniero1
4.0 out of 5 stars Worth Reading
Excellent book but very American centred
Published 4 days ago by bruce steer
3.0 out of 5 stars An interesting read written without the jargon of a lot ...
An interesting read written without the jargon of a lot of math/statistics books. I suppose for some people not knowing the details of some equations would keep the flow, but I... Read more
Published 4 days ago by Tantor
2.0 out of 5 stars Glad that I checked this out from the library first
Odd that there is no mention of the works of John Allen Paulos......he seems to be plowing the same fields but without as much rigor as Paulos. Read more
Published 6 days ago by Daniel L. Wilson
5.0 out of 5 stars dense but comfortable to wrap your mind around
Well written, dense but comfortable to wrap your mind around.
Goes on my list of favorites, I'm passing it on for my friends to read.
Published 6 days ago by jjellen
5.0 out of 5 stars This book has been unfairly criticized
for becoming less "interesting" as it proceeds. This is counter to the reality: in actuality the book becomes *more* interesting as it proceeds, just that it perhaps... Read more
Published 7 days ago by (m)
4.0 out of 5 stars Engaging, instructive and funny
This book is as much entertaining as it is instructive. It is very engaging and would, I think, appeal especially to anyone with a curiosity about the workings of chance as in... Read more
Published 8 days ago by R. Sahmel
3.0 out of 5 stars over-promises?
I enjoyed Part 1 but not Parts 2 - 5. Since I only skimmed Parts 3-5, I'm giving the book an extra star as 'benefit of the doubt'. Read more
Published 12 days ago by Steve
5.0 out of 5 stars Five Stars
superb book!
Published 13 days ago by Sumeet Rohatgi
5.0 out of 5 stars Five Stars
It's good.
Published 15 days ago by Flashlight
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More About the Author

Jordan Ellenberg is a professor of mathematics at the University of Wisconsin-Madison, with a Ph.D. in mathematics from Harvard and an MFA in creative writing from Johns Hopkins. His areas of research specialization are number theory and algebraic geometry. He has written articles on mathematical topics in the New York Times, the Washington Post, Wired, the Wall Street Journal, the Boston Globe, and the Believer, and is a regular columnist for Slate.

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