How Not to Be Wrong The Power of Mathematical Thinking

How Not to Be Wrong The Power of Mathematical Thinking ❰PDF / Epub❯ ✅ How Not to Be Wrong The Power of Mathematical Thinking Author Jordan Ellenberg – The Freakonomics of math—a math world superstar unveils the hidden beauty and logic of the world and puts its power in our handsThe math we learn in school can seem like a dull set of rules laid dow to Be eBook ↠ The Freakonomics of math—a math world superstar unveils the hidden beauty and logic How Not MOBI :º of the world and puts its power in our handsThe math we learn in Not to Be Kindle Ö school can seem like a dull set of rules laid down by the ancients Not to Be Wrong The PDF/EPUB or and not to be uestioned 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 itMath 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 And how likely are you really to develop cancer How Not to Be Wrong presents the surprising revelations behind all of these uestions and many 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 GodEllenberg 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 meaningful way How Not to Be Wrong will show you how.

10 thoughts on “How Not to Be Wrong The Power of Mathematical Thinking

  1. Stuart Stuart says:

    Here's the deal If you're a social scientist or a physical scientist me who works outside the world of controlled laboratory data you have to make sense of the world with imperfect experiments You often have limited data you can't repeat your experiments and the differences between your subject and control are sometimes very fuzzy Yet you have to try to make some inferences even though imperfect data are all you have How do you do that in an honest and careful way? That's what How Not To Be Wrong is aboutHow Not To Be Wrong is in terms of uality of prose the best written book on applied math and statistics I've ever read The author has an MFA as well as a math PhD so maybe that's not surprising The title isn't uite right though The book is really about how to try to be right even though you know you're going to make mistakes now and then That's not as catchy a title I know There's a lot of useful and thoughtful material here mixed in with the elegant writing It's not really a layman's book although it's being sold that way That's OK Those kinds of books like Freakonomics are usually awful and filled with junk analyses This one on the other hand is filled with good stuff It isn't a perfect book There are occasional glitches That's OK too Math geeks especially math geeks who love a good sentence will love it I hope that social scientists and scientists who use and often abuse math and statistics read it as well

  2. Will Once Will Once says:

    I so wanted to like this bookIt's a topic I enjoy I flicked through the book and the author was saying things that I agree with Jordan clearly knows what he is talking about All the signs were goodSo why the 3 stars? Because the book is unfortunately uite dull There are long sections where Jordan spends ages proving some mathematical point or other but then he doesn't draw any conclusions from itHe starts with a story about school kids not liking mathematics because they can't see the relevance to their lives and then he gives us a book which largely proves that the kids were right Some of his explanations are linked to something useful and real world but most are notAnd when he does make a point sometimes he wants to hammer that point in with explanation after explanation It's as if he is trying to batter us into submission with repeated hammer blows Yeah yeah I got itThe writing varies from uite readable to fairly turgid At times it feels like we are wading through a text bookThe title is a complete misnomer If you are looking for a practical guide on the use of mathematics then look elsewhere This does not tell you how not to be wrong Please please either write a book to fit the blurb or change the blurb This does not do what is says on the tinDisappointing There is a good book in here but it needs a much stronger edit to make it readable And it needs to be linked to real life So it's a three star for me The content ought to make it a five star book The writing and limited conclusions drag it back to three

  3. David David says:

    This is a wonderful book about mathematics and its application to everyday life Jordan Ellenberg shows that the certainty that people associate with math is often misplaced; some areas of math are devoted to uncertainty and that's where things get very interestingEllenberg starts the book with a beautiful example of application of mathematics logic and thinking out of the box During World War II a group of mathematicians working for the Statistical Research Group were given a problem by some Air Force officers Fighter planes returning from missions were analyzed for bullet holes The number of bullet holes per suare foot were counted For example there were 111 bullet holes per suare foot in the vicinity of the engine 173 in the fuselage 155 in the fuel system and 18 in the rest of the plane The officers wanted to add some armor to the planes; the uestion was where? The planes could only support so much weight and where would additional armor be most advantageous? The officers thought that since the fuselage had the greatest density of bullets that would be the logical location for armor A mathematician named Abraham Wald said exactly the opposite; armor is needed where the bullet holes aren't namely around the engines Planes with lots of bullet holes in the engine did not return at allThe book discusses the issue of statistical significance Scientific experiment often use a 95% confidence threshold as an indicator of statistical significance This means that if a truly random outcome were expected a positive correlation would be seen only 5% of the time Ellenberg includes an xkcd cartoon that shows how easy it would be to perform a set of experiments that could come up with statistically significant results like Green jelly beans linked to acne at the 95% confidence levelSome of the section and chapter titles are hilarious For example in the chapter titled Are you there God? It's me Bayesian Inference Ellenberg brings up a scary example of the use of big data Based on a teen age girl's purchases of unscented lotion mineral supplements and cotton balls the retail store Target began sending her coupons for baby gear because of the correct inference that she was pregnant Another great section title is One thing about God then I promise we're doneAnother interesting title is The Cat in the Hat the Cleanest man in school and the creation of the universe in which Ellenberg reviews some of the probabilistic arguments for and against the existence of god And I love the famous uote by Richard Feynman You know the most amazing thing happened to me tonight I was coming here on the way to the lecture and I came in through the parking lot And you won't believe what happened I saw a car with the license plate ARW375 Can you imagine? Of all the millions of license plates in the state what was the chance that I would see that particular one tonight? Amazing I also love the chapter title If Gambling is exciting you're doing it wrong Ellenberg describes how several groups capitalized on several state lotteries Due to some strange lottery rules it is was? possible to reliably make a profit given enough investment of resources No illegal shenanigans the states make money no matter what you do You could make a profit by taking advantage of the rules and of the people who buy lottery tickets without a coherent strategy And I did not realize that Voltaire made his fortune by taking advantage of state lotteriesEllenberg brings up the phenomenon of Nate Silver predicting the outcome of the Obama vs Romney election Silver predicted the probability of both candidates winning state by state along with the margin of error By adding up the probable errors he estimated that he would be wrong by 283 states Critics seemed to have ignored the fact that he was not wrong by this many states in fact he correctly predicted the outcome in all 50 statesI highly recommend this book to all people who are even vaguely interested in math probability logic and the application to everyday life This is an excellent book

  4. Kara Babcock Kara Babcock says:

    I math for a living I mathed both amateurly and professionally at school I math uite a bit And as a math teacher I like reading pop math books that try to do for math what many science writers have done for science So picking up How Not to Be Wrong was a no brainer when I saw it on that bookstore shelf I’ve read and enjoyed some of Jordan Ellenberg’s columns on Slate and elsewhere some of them appear or are adapted as chapters of this book And he doesn’t disappointI should make one thing clear I mainlined this book like it was the finest heroin Partly that’s because I just love reading about math but in this case I was also days away from moving back to Canada from the UK when I started this and luggage space was at a premium so I was on a deadline to finish this book I injected chapters at a time into my veins revelling in that rush as Ellenberg charismatically and entertainingly explores the math behind a lot of everyday concepts and ideas Unlike similar attempts however Ellenberg doesn’t pull the punches He’s than willing to go into the higher concept ideas behind the math and when it starts getting too esoteric or academic even for this venue he’s always ready with a book recommendation for those interested in some further readingEarly in my reading I tweeted I had already decided to give this book five stars because Ellenberg alludes to Mean Girls in a footnote Specifically he says “As Lindsay Lohan would put it ’the limit does not exist’” That’s really all you need to know about Ellenberg’s writing style and sense of humour Actually I’m not all that enamoured with the footnotes in general; they interrupted the flow of my reading and the symbols used to mark them were slightly too small so I kept missing them in the text—but that’s a design issue The content of the footnotes themselves is often informative or as in the case above humorous Ellenberg might be a university math professor but he also has a sense of humour and an awareness of pop culture that helps to make his writing accessibleI’m impressed by the way Ellenberg effortlessly straddles pure and applied mathematics The child of two statisticians he clearly has a good grasp and appreciation of the way applied math drives so many areas of society From economics to gambling he makes passionate appeals for informed perspectives over simplistic analogies or fallacies His first chapter criticizes analogies that promote linear thinking about taxation when the very same economists writing these analogies know that taxation probably isn’t linear He doesn’t argue for or against an increase in taxes but rather he points out that it’s wrong to oversimplify the concept when trying to sell it to the public Is a curve really all that much harder to understand than a line?There’s also some great chapters on odds and the lottery in which Ellenberg recounts how a group of MIT students set up a legitimate operation to bulk buy lottery tickets from a certain game that actually gave them good odds of winning They made a profit because they used math to turn a game of chance into a predictable investment strategy which is than we can say for the stock market So you know stay in school kidsBut actually the parts about the lottery that impressed me were towards the purer end of the math spectrum Ellenberg started discussing for example how best to pick the numbers on one’s tickets so that one could maximize the chance of winning at each tier of prizes It turns out that it’s possible to represent the way of picking these numbers geometrically yes as in pictures and that it’s related to the way we create error correcting codes which allow us to send instructions to spacecraft and compress data in JPEGs MP3s and on discs He goes into uite a bit of detail about the advanced concepts behind these ideas Later he points out how correlation on scatter plots corresponds to an ellipse—and we know how to deal with ellipses algebraically which gives us a good toolset for talking about correlation algebraically tooSo How Not to Be Wrong makes an effort time and again to belie the impression that we often get in school that math consists of a series of discrete topics arithmetic geometry statistics and the dreaded algebra We teach it that way because it’s easier to lay out as a curriculum and focus on the essential skills of each discipline And also because we are boring If you’re lucky like me then as a student you’ll start to see the connections yourself Circles and pi start showing up everywhere to the point where suddenly you feel like you’re being stalked and no amount of infinite series or integration is going to save you But really good teachers start showing these connections as soon as possible We fail students and leave them behind because in our rush to euip them with the skills we’ve been told they need we rob them of the idea that math is a creative process instead fostering this false impression that math is a sterile difficult procedural slog If it is then you might be a computerEllenberg never demands a knowledge of integral calculus of set theory or of transfinite numbers What he does demand is an open mind a willingness to be convinced that not only does math have a useful place in life it’s pretty obvious to most people that someone needs to know how to math; they just don’t see why it should be them but that a deeper understanding of the roles and uses of math can enrich anyone’s life One can be a believer in the power of mathematics without necessarily worshipping at its altar and it’s this uest for adherents rather than acolytes that makes this popular math book successful It helps that Ellenberg’s style is witty It helps that he is passionate without sounding too evangelical He weaves in enough history anecdotes and allusions to demonstrate that mathematicians’ journeys and the development of mathematics as a discipline has been just like everything else in life alternately dramatic and dull intense occasionally acrimonious We don’t like to admit it but we mathematicians are people too And occasionally we’re wrong very wrong like those nineteenth century French eugenicists The title here is tongue in cheek and How Not to Be Wrong can’t guarantee your future correctness with great certitude All it can do is help you think critically logically but creatively about the problems and uestions that you’ll face in the future Because mathematics is a tool for helping us to do amazing things You can be a novice or you can be a proficient user of this tool but either way you’ll need to pick it up at some point to do a little handiwork Don’t fear it embrace itOh and read this book

  5. Ian Ian says:

    This book was an excellent guide to the many ways in which our intuitions and poorly understood statistical training can lead us astray One of the areas that it covers is regression to the mean a concept which pretty much everyone needs to be aware of since a better awareness of its ubiuity would prevent a lot of errors Among other things this concept explains why a successful pilot study is likely to give worse results when rolled out why a good performance is often followed by a worse performance and vice versa why seuels are less successful and so on The book also explains why a lot of medical research is effectively inconclusive despite statistically significant results and how p values are generally misinterpreted so we should take medical research with a large grain of salt Some of the other areas the author discusses are counter intuitive One topical example is that if there are three or options then unless one option has an absolute majority in its favour then ALL of the options will have a majority opposing them which explains why politicians can never please everyone For example if the government offers three options for reducing the deficit a increase taxes b cut health funding c cut welfare funding and eual numbers of people favor each option then 66% of people will be opposed to each option so nothing the government does will please a majority This book is full of gold for anyone who hasn't encountered some of these concepts before such as the story of Abraham Wald's insight regarding how the missing bullet holes determined where bombers should be armoured during WWII or how the Laffer curve governs a lot of phenomena rather than linearity or how a zero correlation doesn't necessarily mean that there is no relationship between two variables correlation co efficient does not detect non linear relationships or the story of why scientists took so long to be certain of a link between smoking and lung cancer not because of obstruction by the tobacco companiesAlthough I am trained both as a mathematician and statistician you don't need a strong mathematical background to understand and benefit from this book Most examples reuire basic arithmetic and the author has a talent for producing crude but enlightening graphics that help to guide the reader's intuitions In addition to this book I would recommend pretty much any recent book by Gerd Gigerenzer whose work shows how scarily ignorant doctors are of how to properly interpret results of medical tests and why mass screening programs do significant harm while not significantly reducing mortality

  6. Amit Mishra Amit Mishra says:

    Mathematics is a piece of music the deeper you allow yourself to understand its lyrics you will understand the practicality of it in real life It can be a dull and unimaginative concept that only deals with some of the already established formulas It paved a way for people to live their life hassle free It brings the practicality and scientific conclusion on any topic whether it's about calculation for about judging a person With probability and numbers it makes us our life comfortableThe author has done a tremendous job to bring out the real life benefits of Maths

  7. Maryanne Maryanne says:

    Where language and math meet is where my head explodesThat's this bookFortunately the author has a funny down to earth style that keeps me going even when my eyes glaze over and start to roll back into my head That has nothing to do with him; it's all me He and I have a fundamental difference in wiring he loves numbers and the things they can do For him they sing For me they are instruments of torment and deceit Let me give you an example Here's one from page 44 et se where he demonstrates that the sum of an infinite string of ones 11 11 1 euals zero except that it might also eual 1 Or maybe it's actually 12 You heard me the sum of an infinite string of whole numbers is a fraction And they say that numbers are immutable and true and solid unlike MY stock in trade words with their shades of meaning and the ease with which they can be manipulated HABut you cannot frighten me away so easily sirThis is a challenging book than say Nate Silver's because it gives you the method the math behind the theories That should not scare you It should dare you Along the way you'll be confused and befuddled but you'll also laugh and be intrigued and remind yourself that the ways in which you think you know really KNOW the world are hopelessly flawed and this guy can prove it If nothing else this book is endlessly valuable for that

  8. WarpDrive WarpDrive says:

    Enjoyable entry level book particularly recommended to any lover of applied maths who did not get prior significant exposure to the main concepts of statistics and probability calculusThe author writes in a very engaging and conversational manner and his enthusiasm for maths is uite contagious; I like how he manages to compellingly convey the message that math is a creative process not a sterile procedural slogWhile the book is designed to be understood by a wide audience so it is necessarily kept at a pretty popular level which disappointed me a little bit to be honest as I was expecting something meaty from a purely mathematical perspective I must nevertheless admit that there are some subjects of the book that are brilliantly explained with lucid clarity the author's treatment of the application of statistical techniues to number theory is nothing short of fascinating for example; and his explanations of the basic concept of Bayesian inference of projective geometry and of the Buffon needle problem are masterful Chapters 18 when he deals with the concept of axiomatic postulating deduction and self contradiction is a real gem where by the way his neo Platonist view of mathematics comes to fore view to which I full subscribe The final chapter is also great and it represents a passionate defence of mathematics and rationality as fundamental tools for a sceptical commonsensical balanced realistic view of reality as opposed to the false ideologically motivated certainties that permeate some circles and at which the author pokes some great fun

  9. Peter (Pete) Mcloughlin Peter (Pete) Mcloughlin says:

    Makes a good case for the real world of advantages of having a mathematical understanding and how to work with math concepts The author argues that math is a very strong version of common sense reasoning which can keep a person sharp and savvy in a complex world

  10. kartik narayanan kartik narayanan says:

    I am one of those fortunate individuals who cherishes and loves Mathematics in all its forms But I know a lot of people for whom the Maths is a dreaded specterWhy is that so? Inevitably this is a problem that arises from the way the subject has been taught And this is what the book tries to dispel This book takes us behind the numbers euations theories and abstruse concepts to show the practical applications of whatever we have been taught Along the way the history of these various ideas are explained as are various anecdotes which are informative and amusingThis book is written along similar lines to Metamagical Themas and GEB while not at the same level Think of this book as a stepping stone to the fore mentioned booksThe book deals with concepts that we have been taught in our 11th12th Graduation The author doesn’t really dumb down the concepts – this means that while they have been explained well the reader really has to concentrate while reading the bookAnother facet of this book which made me love it were the lovely uotes from history A couple of examples are belowWhen talking about the romantic notion of how mathematicians are portrayed as genius loner types the author uotes Mark Twain – “It takes a thousand men to invent a telegraph or a steam engine or a phonograph or a telephone or any other important thing—and the last man gets the credit and we forget the others”When talking about the need to focus on practical applications the author uotes Theodore Roosevelt –“It is not the critic who counts; not the man who points out how the strong man stumbles or where the doer of deeds could have done them better The credit belongs to the man who is actually in the arena whose face is marred by dust and sweat and blood; who strives valiantly; who errs who comes short again and again because there is no effort without error and shortcoming; but who does actually strive to do the deeds; who knows great enthusiasms the great devotions; who spends himself in a worthy cause; who at the best knows in the end the triumph of high achievement and who at the worst if he fails at least fails while daring greatly so that his place shall never be with those cold and timid souls who neither know victory nor defeat”The author Jordan Ellenberg is a mathematical prodigy He has deftly weaved the concepts with good writing to bring out the inherent joy in mathsPeople interested in Big Data have to definitely read this book For those who hated mathematics when growing up and now want to figure out what the fuss is all about and those who just want to enjoy a good read this book is brilliant

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