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How Not to Be Wrong: The Power of Mathematical Thinking Paperback – Illustrated, May 26, 2015
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“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.'” —Mario Livio, The Wall Street Journal
“Witty, compelling, and just plain fun to read . . . How Not to Be Wrong can help you explore your mathematical superpowers.” —Evelyn Lamb, Scientific American
“A poet-mathematician offers an empowering and entertaining primer for the age of Big Data . . . A rewarding popular math book for just about anyone.” —Laura Miller, Salon
“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.” —Nature
“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.” —Times Higher Education
“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.” —Kirkus Reviews
“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.” —Booklist
“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 Pinker, Johnstone Family Professor of Psychology, Harvard University; author of How the Mind Works
“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.” —Steven Strogatz, Schurman Professor of Applied Mathematics, Cornell University, and author, The Joy of x
“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.” —John Allen Paulos, author of Innumeracy and A Mathematician Reads the Newspaper
“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.” —Timothy Gowers
“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." —Rebecca Newberger Goldstein, author of Plato at the Googleplex
"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!" —Danica McKellar, actress and bestselling author of Math Doesn’t Suck and Kiss My Math
“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.'” —The Guardian
About the Author
- Publisher : Penguin Books; Illustrated edition (May 26, 2015)
- Language : English
- Paperback : 480 pages
- ISBN-10 : 0143127535
- ISBN-13 : 978-0143127536
- Reading age : 18 years and up
- Item Weight : 13.6 ounces
- Dimensions : 1.1 x 5.4 x 8.4 inches
- Best Sellers Rank: #10,635 in Books (See Top 100 in Books)
- Customer Reviews:
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Top reviews from the United States
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How Not to Be Wrong shunts the reader smoothly and with refreshing humor between geometry, military history, computer science, politics, statistics, gambling, medicine, morality, and philosophy. I emerged at the end shaking with not only a wealth of new information about all these stops on the rail, but with the conviction than now I know what they’re for. Science doesn’t tell you what you ought to believe; it tells you what you ought to do. We don’t vote to determine the best leader; we vote to give everyone an excuse to continue not committing crimes. The best way to treat your most cherished beliefs is by attempting to disprove them.
I know that all sounds like nonsense, but I honestly can’t think of a more concise or convincing way to talk about Ellenberg’s insights than the book that he wrote. Start with plotting a line, and end with the reason you get up in the morning.
I recently graduated, and I still listen to this audio book because the information is so rich and varied. It's a really easy way to keep your general skills sharp. This books isn't full of numbers and symbols, so I wouldn't recommend it for people who need to learn the actual math.
The common misconception is that the math we learn in school is useless and it is taught to teenagers to simply torture them. Math can be difficult but it can be extremely interesting. There are numerous resources today on the internet that display the marriage between reality and math, but this book gives its readers a deep dive into the treasures of mathematics.
This book is incredible. Every chapter is better than the last. From how to keep planes from being shot down to winning democratic elections, this book covers it all. The only area I didn’t find particularly interesting was the pages on the lottery. Obviously, this is an easy way to discuss probability but to sum it all up concisely: you have a very small chance to win the lottery though there are ways to increase your chances from never to almost never.
You do not have to love math or statistics or science to like this book. You would probably enjoy this book more is you hate math. The author is incredibly smart but importantly, he is a great communicator.
Top reviews from other countries
1. Survivorship bias – average return on investment funds for example - omits the funds that were so unsuccessful that they were closed – so that only survivors data is analyzed resulting in a false impression;
2. Sometimes a line is actually a curve or a parabole. About the risks of linear regression (continuous increase of population is not a straight line but a curve so that the expected rate of growth will be reduced);
3. A small selection will produce more unexpected results – for example smaller population states have the most extreme ratios for cancer – both low and high – but this is just another result of randomness and does not give any important insights;
4. Law of large numbers revisited from several angles;
5. Don’t talk about percentages of numbers when the numbers can be negative. The example is job growth by sectors – lets say retail sector adds 10 jobs, construction loses 10 jobs and IT adds 2 jobs. The total job adds are 2 people. So if you would want to manipulate the data you could say that all the jobs were created in the IT sector, because the total job growth is the same as the IT sector growth;
6. There was another warning about getting fooled by randomness: a stockbroker sends different stock tips to a large number of recipients and does this over and over. There will be a few recipients who will get stock tips that were right again and again. So the stockbroker can seem genius because no-one will be able to know about all the wrong suggestions;
7. Bayesian inference. A fancy name in order to impress at smalltalk but basically means a statistical test which is done on the same data but after some new input has emerged;
8. p-values. How to test the reliability of scientific statistical studies. Turns out that there still are many unreliable studies published;
9. There was also a big discussion on the election systems in different countries. Basically the paragraph showed how in many cases the system modifies the initial process in such a way that the most popular candidate may not win.
A few general comments:
1. It is mostly a very boring book and although it contains lots of important intelligence then because of the books marketing I was hoping for much more entertaining read;
2. I made lots of notes in the book but there was a big gap from about page 189 to 272 when it just got too theoretical.
3. Although the book should show us the maths in everyday life it seems to be mostly intended for math scientists in order to show to their kids that their work has some real life connection instead of showing to the rest of us to apply math concepts in real life. Do not get me wrong, it has this value also, but there is just too much of theoretical math.
Ich spreche fließend Englisch und lese sehr viele Bücher, meist Englisch.
Meine Mathematik-Kenntnisse sind eher tiefergehend (Promotion im
Bereich der numerischen Mathematik / Ingenieurwesen).
Die English-Kenntnisse sind notwendig, die Mathematik-Kenntnisse absolut nicht.
Ich bin Skeptiker und versuche Menschen immer wieder zu erklären, wie
man in die Irre geführt werden kann, wenn man nicht in Wahrscheinlichkeiten
denkt. Dafür gibt das Buch ausreichend Munition.
Das Buch ist sehr gut und unterhaltsam geschrieben und es sind
keine tiefgreifenden mathematischen Kenntnisse beim Lesen und zum Verstehen
notwendig. Man sollte allerdings eine gewisse Affinität zur Statistik haben. Das
Buch hat etwas von den Büchern von Gero von Randow zum Thema des Ziegenproblems.
Fazit: Für mich steckt da eigentlich nichts neues an Erkenntnissen im Buch, aber die
praktischen Beispiel aus dem Alltag und der Forschung sind super eingängig. Wer also
schon immer verstehen wollte, wie eigentlich intelligente Menschen Bücher zum Bible-Code
schreiben können (absoluter Blödsinn, den ich nicht kenne, der sich aber millionenfach verkauft
hat, glaube ich), der ist hier richtig.
Klare Kaufempfehlung! Viel Spaß beim Lesen.
Unfortunately, this was the most interesting example in the book. The book has other examples, for sure, and, as you would expect, it also highlights other areas where our intuition or "logic" is wrong. But, these examples, at least for me, were much less interesting. The US elections are one area it talks about in more detail.
If I'm honest, this book reminds me why I had to drop A Level maths after 3 months i.e. because I wasn't very good at it, didn't enjoy it, and found it to be "too much hard work". Perhaps that's not the best approach to difficult things, and maybe I wish I had persevered with the A Level, but I did find this book to be quite hard work. As the author claims at the start, it isn't packed full of equations, but it does get into some detail around things like probability, which I have twice studied at university (BSc and MBA), but still found difficult to follow. I think part of the challenge is that, for me at least, this book needed to be "studied" rather than just "read", and I didn't want to study it. If you're more literate in Maths, that may not apply to you, and it may be an easier read.
Parts of it were certainly interesting, and I read the whole 430+ pages because I know that there are important ideas / lessons here, even if I'm not smart enough to fully understand all of them (or not motivated enough - probably both).
I wouldn't recommend against the book, I'm just trying to give you a better sense of what to expect. If I'd known what it contained, I probably wouldn't have bought it, to be honest, and I certainly wouldn't have chosen it for my Xmas holidays "easy reading" (it wasn't), but I am also sure I've learned something from it.
My final comment is that I think it's unnecessarily long. The author is clearly 100 times smarter than me, probably more, but I do think he could have made this shorter and still made the same points.
So, overall, I'm a bit disappointed, but perhaps more with myself than with the book. If you're ok with the Maths, give it a go. It's well researched, well thought through and, in places, very funny.
However, my criticism is aimed at the publishers, not the author. The text is a bit small (I'm in my 40s, and the text is only just about legible), and the asterisks (used for the footnotes) are microscopic. Frequently I would get to the bottom of the page and discover that the author had written a footnote. I would then spend a good minute or two trying to discover where the asterisk was in the text, and then have to do some re-reading to remind myself of the context of what the footnote was for, then finally read the footnote. By which point I had lost the thread of the rest of the page, and would need to re-read that before I could progress.
So rather than be a nice little aside (like you would experience when reading a Terry Pratchett novel), each footnote added about 3 or 4 minutes of discontinuity to the reading.