An excellent little book that addresses the way numbers are presented in our society, which as it turns out is in the most overblown and least helpful manner possible. Yes the revelations about numbers aren’t exactly surprising here, but they are nonetheless written about in a humorous manner and do get you thinking.
It does at times start to seem redundant; particularly when the author challenges the idea of precognition, which for this kind of book just seems like far too easy of a target. It is however a great read and recommended for anyone who cynically sighed at tabloids at some point.
A short but highly entertaining book on numeracy. However it is presented in such a way that you want to read more. I suggest it is mandatory reading for all as I am well aware that most people are hazy when statistics are quoted - and in an era where dubious figures are used to gain sales or electoral success it becomes a necessity to recognise statistical lies.
Whilst I am reasonably numerate it is easy to believe that people are generally very much the same and as numerate as I. This however is not the case. Being able to manage numbers used on a day to day basis is not much use when very large numbers are concerned. This is an eye-opening start to the book and provides a glimpse of how complex life is. As an example Paulos gives the example of a human squatting down is roughly a metre in diameter. A cell is the human body is as a human body to the State of Rhode Island*. A virus within a human is as a human is to the Earth!!.
I may not have understood all the fine detail however I was not trying to learn "maths" but to get an impression of what numbers can and cannot do and on that basis it is beautifully ptiched.
*And as a reviewer I looked it up - it is 1,214 sq miles (3,140 km2)
Though written in the late 1980's this book remains relevant because the issues raised are as true now as then. The book focuses on a lack of numeracy as cause of the tendency of many people to have beliefs that don't make sense and cannot stand up to any scrutiny. In this way it differs itself from other books such as 'bad science' which have a broader skeptical approach.
A particular focus is on probability, that basically things are more likely to happen than we intuitively think and that we often make too much of what is really a coincidence. Some of the examples are very interesting and mathematical explanations are easy to follow. It also explains how some scams can work and how statistics such a those found in medical results can be misleading.
The writing style is warm and brisk and not high handed or righteous. The author can also be quite funny both in his observations and in word play.
To me, the most intriguing aspect of this book was Professor Paulos's ability to take simple math concepts that I learned way back when . . . and to show how they could enrich and expand my appreciation of the world around me now. It was like Alice going through the looking glass in the sequel to Alice in Wonderland. There's a lot there that I never imagined. For example, the way disease rates are often described is for those who have survived to 85 years old. If you are younger, your current probability of incidence will be much lower (possibly more than 90 percent lower). Also, you can use the way you design your questions and sample to help eliminate bias (such as by asking about the results of a coin flip and dangerous sexual behavior in the same population). You can also find great humor in the errors of authority figures who misquote probabilities and risks. Plus, you can answer questions that I would never have thought of (such as the likelihood of breathing in an atom that Caesar did). If you are feeling cowed about your math ability, take heart! Most of the concepts here you can handle. For example, can you multiply two numbers together? You can answer "yes" to my question if you can do so with a calculator. If so, you can appreciate almost all of the examples in the book. Professor Paulos has a mind that works differently and more inquisitively from mine, but I enjoyed learning how his thoughts. He thinks about topics like how long it would take dump trucks to excavate Mount Fuji, how many times a deck of cards need to be shuffled to become random, and what the Earned Run Average is for a pitcher who lasts one-third inning and gives up 5 runs. I realized that if I thought about more things like this, I would develop new perspectives on the world. He makes a helpful attempt to create solutions so that more people can appreciate the world in a quantitative sense. These include using exponents to indicate the size of numbers (such as the Richter Scale does for earthquake strength), refocusing secondary math education to practical applications rather than teaching calculus earlier and earlier, having talented mathematicians teach younger people, and disciplining those who communicate in public to check the mathematical accuracy of what they say. What do we lose if we don't? Well, those who don't learn a little math will end up in careers that pay a lot less. Social resources will be misapplied to problems that are less serious (obscure diseases and terrorism get a lot more attention to reducing accidental deaths among young people, which is a greater danger). We will make bad resource decisions in our own lives (such as by playing the lottery without realizing that 50% of the money is not paid out to anyone buying a ticket). I also appreciated how few people can use mathematics in creative ways, to solve problems. For instance, in our professional practice we developed a new way to forecast certain forms of investment behavior. Over 20 years of doing this work, I have never found anyone who could make a single useful suggestion for how to improve the mathematics of our approach, despite having had conversations with dozens of people with advanced math and statistics degrees who would get benefit from an improved approach. I suspect from this experience that there's a higher level of mathematical thinking that Professor Paulos did not explain in his book that we would all benefit from learning. Where do we start? I can hardly wait to learn!
"A million dollars, a billion, a trillion, whatever. It doesn't matter as long as we do something about the problem." Does it matter, or does it not? Perhaps you can more easily visualize what jumping by six orders of magnitude means if you divide it by 10^6: "One dollar, a thousand dollars, a million..."
Or perhaps consider this: Abraham Lincoln was elected to Congress in 1846 and was elected President in 1860. John F. Kennedy was elected to Congress in 1946, and was elected President in 1960. Lincoln's secretary was named Kennedy. Kennedy's secretary was named Lincoln. Andrew Johnson, who succeeded Lincoln, was born in 1808. Lyndon Johnson, who succeeded Kennedy, was born in 1908. John Wilkes Booth, who assassinated Lincoln was born in 1839. Lee Harvey Oswald, who assassinated Kennedy was born in 1939. There is some mysterious harmony ruling the world, isn't it?
Most likely not. Politicians' careers do follow certain patterns - people are very rarely indeed elected presidents at 19, then elected to congress at 86. Furthermore, there are very few records of assassins in the age group over 65, for instance. You also have to take into account that, taking into account US constitution, there is nil probability that Kennedy would have been elected president in 1961, or 1958. And Lincoln isn't all that uncommon as the last name, is it? And finally, we have been rather selective which facts we have included: Abraham Lincoln was born in 1809 and died in 1965, while John F. Kennedy was born in 1917 and died in 1963, for instance, but along with all other facts this simply didn't fit the intended story, so it was omitted.
Throughout the book, Paulos tries to demystify such mysterious occurances by providing more or less elaborated examples, where he applies combinatorics, probability and statistics. All relatively simple concepts, but people tend to forget about them once they leave high school. Is it true that if the flipped coin has come up heads for fifteen consecutive rows, it is much more likely to come up tails on its next flip? And what about the statistics claiming that one out in eleven women will develop breast cancer, on the average?
Some sections - whining about the incompetent elementary school math teachers etc. - are too whinny for their own good, but otherwise this short booklet is a fun read. But then again, with a degree in physics, I probably already fall among the numerate. What I was very much missing, though, is a list of references from which professor Paulos has taken his examples from.
Sadly this book will probably not be read by the people who would gain the most out of it, those who are terrified of numbers. Innumeracy is the one state of ignorance which is seen as socially acceptable. Paulos presents a strong case that mass innemeracy is a severe problem in modern society (he mostly refers to his own country, the USA, but the case is just as true in the UK) and the effects are all too real.
Basic misunderstandings of probability for example seriously impacts the ability of people to make rational life choices, Paulos uses the example of people who are too afraid to fly because they fear terrorism when the dangers are absolutely minescule in comparison to the danger of choking to death. The susceptiblity of the innumerate to psuedoscience is another Paulos bugbear.
The only downside to the book is that I can't honestly claim that it got me thinking about the subject for more than five minutes after I finished it.