Innumeracy: Mathematical Illiteracy and Its Consequences by John Allen Paulos (PDF)

Description

Why do even well-educated people understand so little about mathematics? And what are the costs of our innumeracy? John Allen Paulos, in his celebrated bestseller first published in 1988, argues that our inability to deal rationally with very large numbers and the probabilities associated with them results in misinformed governmental policies, confused personal decisions, and an increased susceptibility to pseudoscience of all kinds. Innumeracy lets us know what we’re missing, and how we can do something about it.Sprinkling his discussion of numbers and probabilities with quirky stories and anecdotes, Paulos ranges freely over many aspects of modern life, from contested elections to sports stats, from stock scams and newspaper psychics to diet and medical claims, sex discrimination, insurance, lotteries, and drug testing. Readers of Innumeracy will be rewarded with scores of astonishing facts, a fistful of powerful ideas, and, most important, a clearer, more quantitative way of looking at their world.

User’s Reviews

Editorial Reviews: Review “Our society would be unimaginably different if the average person truly understood the ideas in this marvelous and important book.” ―Douglas Hofstadter“[An] elegant … Survival Manual … Brief, witty and full of practical applications.” ―Stefan Kanfer, Time About the Author John Allen Paulos, professor of mathematics at Temple University and the author of several other popular books on mathematics, is a regular contributor to national publications, including The New York Times and Newsweek. He lives in Philadelphia, Pennsylvania.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐John Allen Paulos passionately explains in a personal essay the probabilistic nature of life. He believes that too often people are innumerate and have many misconceptions about math. He enumerates these fallacies in the preface (Paulos, xii,xiv):1. Math is nothing more than computation;2. Math is a completely hierarchical subject;3. Storytelling is not effective as an educational tool in mathematics;4. Mathematics is only for a few;5. Math numbs or limits our freedom.Since Paulos studied philosophy as an undergrad and mathematics in graduate school, he respectfully acknowledges the duality of the two disciplines. Throughout the book he makes comparisons such as “The romantics believe that a concern with numbers numbs us to the big questions of grandeur of sunsets and waterfalls” (Paulos, 179).Paulos provides real world examples of innumeracy in subjects like stock scams, choice of spouse, newspaper psychics, diet, medical claims, lottery, astrology, drug testing, insurance and law. At times the reader must patiently muster through detailed proofs. But, don’t worry as Paulos promises “there won’t be a test” (Paulos, xiv). Be patient, just rest and relax while reading “Innumeracy” then will you thoroughly enjoy it. If you are among the innumerate then simply read through the math formulas without a concern for grasping the conceptual depth. John Allen Paulos is flexing his numerate muscles giving Innumeracy greater strength.The author’s aim is to make each of us less intimidated by the numbers. He begins by familiarizing the reader with the basis of counting: how many people are in the US; how many people in the US are under 18, how many die each year; how many cigarettes are smoked each year; and how many words are there in a good sized novel?Many of us believe incorrectly in the magic of coincidences. However, there are no coincidences instead statistical probabilities. For example in a room of 23 random people – 2 or more will have the same birthday. Another example is the old adage “everything comes in threes” (Paulos, 69). Again this is just statistical probability since if you wait long enough things will come in sets of three. Another misconception is the “why me?” attitude toward misfortunes. Bad things happen periodically, the probability is that they’re going to happen to somebody, why not you?”The tendency to attribute meaning to phenomena governed only by chance is ubiquitous” (Paulos, 114). The fruitful example the author uses to illustrate this concept is regression to the mean. Regression to the mean is the tendency for an extreme value of random quantity followed by a value closer to the mean. In this case he provides the example of very intelligent people who may have intelligent offspring, yet generally will be more likely to be less intelligent than their parents.John Allen Paulos has an affinity to number ID over name as a means of identification since no two people can have the same ID number. However, he is appalled by the use of an excessive number of digits. In being numerate one would know that an identification number with 9 digits will have 109 (one billion) possible different numbers.Innumeracy covers relative risk, which is a significantly large issue for Public Health and the future of health care. This interesting passage in the book proposes that a logarithmic safety index be used. In this way we would be measuring the relative safety against the relative danger adding on the likelihood of the endeavor.Innumeracy is not a romantic beach read. Its meager attempt to be sexy is the argument over the “bell-curve” where “the urge to average can be seductive” (Paulos, 169). The appeal of this book comes from the nature of the author’s experience in having studied philosophy, literature and mathematics. Paulos is a believer in the human condition, specifically the tendency to want it all. Numeracy will help people understand that there are going to be trade-offs. A romantic at heart he adamantly opposes the view that mathematics is esoteric and those that study numbers are “coldly rational”. The author’s desire is to stimulate numeracy and enhance the appreciation of the probabilistic nature of life. John Allen Paulos is a best selling author, public speaker, columnist for […] and Guardian and a professor of math at Temple. He offers his web address and welcomes feedback […]

⭐We should expect our leaders — in business, in the public sector, in the household — to be driven by an interest in facts and data. In the process we should, as Paulos puts it, be able to at least “deal comfortably with the fundamental notions of number and chance.” This is basic mathematical literacy, and his book lays out a list of consequences from our failure to place enough importance, collectively, on understanding the general math that governs our world and our work and, as importantly, the statistics we use to describe it.The value here is less in being about to perform complex or even intermediate calculations — although that certainly has its place in many professions. For most of us, it’s more about being able to contextualize numbers. This is critical in, to pick one professional sphere, public policy and administration. If a policy maker raises the prospect that 500 deaths over a holiday weekend represented a “carnage” that justifies new laws or regulations, a distressingly high number of us would not be positioned to identify his or her mistake via the “broad base fallacy” (where 500 deaths was on par with a typical holiday weekend where millions of people undertake countless activities, each of which carry a minor chance of death).Paulos, a mathematician at Temple and author of a handful of accessible books along similar lines as Innumeracy, spreads himself a little thin across his illustrative examples. I suspect the narrative weave from one topic to the next would’ve been aided by the use of fewer examples that he returned again and again in varying contexts. (I exclude the example of coin flips, which he uses often and which is every statisticians’ go-to example.) But, broadly, Innumeracy hits its mark and I thoroughly enjoyed and recommend it. It’s a clear look at the value of scientific and mathematical literacy, something those who have invested effort to achieve know provides real world value. If we, as a society, could more easily carve through news stories based on flimsy statistics, we’d be better positioned to contextualize, discuss, and act on, our more pressing challenges. Paulos suggests media outlets themselves try employing “statistical ombudsmen” to help filter the real numbers from the bad before they get to work describing the world for viewers, listeners and readers, and I wholeheartedly agree.

⭐My own failure to notice the subtitle of this book led me to hope that it might remedy my own innumeracy. Alas, it is a work that bewails the ubiquity of innumeracy in today’s world and laments some of the consequences of this phenomenon.It has in no way alleviated my aversion to numbers. It has, however, taught me to be more critical of dubious statistical claims. For this I am grateful to the author.He has managed to make an engaging read out of subject that many might otherwise regard as dull.

⭐A really great book and you can certainly learn a lot. The reason for the 4 stars and my only issue is that there are chapters about the education system and how it can be improved, specifically when it comes mathematics. And while I agree with the points made by the author, I don’t think it fits the tone of the rest of the book. It’s like you have started reading a completely different book and you end up wondering how long until it goes back to the way it was (if at all).

⭐Fantastic for those who like mathematics and science/critical thinkingEssential for those who don’tIf you don’t Ever ask the question “what do you mean” or “where did you get that from?” Then this book will explain to you why these questions are importantSmaller than I’d have thought but a lot is packed into itAlso you don’t need to be a maths whizz to understand it but there are basic mathematical principles you should know to help you get through it – particularly the language of maths

⭐I thoroughly enjoyed this book. Although my daily work involves interpretation of numbers and statistics, I haven’t studied Maths in any formal way since ‘O’ Level in 1979 and I had no problem following the concepts and logic.John Allen Paulos has the happy knack of taking one through a process to a potentially complex level in easy-to-understand and logical stages. The book really does make one realise that there’s no reason why anyone should be able to say “I just don’t get Maths”. Unfortunately, the problem appears to stem from Primary school teachers who often lack confidence themselves in Maths and either fail to explain basic concepts or fail to engage and enthuse young children. By the time children have access to specialist Maths teachers at Secondary school, they are often confused and feel uncomfortable with mathematical concepts and, for many, there’s no way back!This book should be required reading for any educationalist or prospective / working teacher.

⭐Every politician and policy maker should read this book. Most of us are guilty of the sort of shortcomings in understanding mathematics that this book highlights in a very readable and entertaining fashion. Some of the references are a bit dated now – I think it came out in the 1970s – but the bulk of the material is still highly relevant. Interesting fact: one million seconds is about 12 days; one billion seconds is about 32 years. People simply do not appreciate the enormous difference between a million and a billion. Why? – because they are innumerate.

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